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zysi [14]
3 years ago
10

Which graph represents the following piecewise defined function?

Mathematics
2 answers:
ss7ja [257]3 years ago
9 0

Answer:

D

Step-by-step explanation:

kenny6666 [7]3 years ago
5 0
The correct answer is shown in attached figure
To find the correct graph, we should study the continuity of the function

Check the continuity at x = -2
from the left ⇒⇒ f(-2) = 1/2 * -2 + 3 = 2
from the right ⇒⇒ f(-2) = 2
∴ The function is continuous at x = -2

Check the continuity at x = 3
from the left ⇒⇒ f(3) = 2
from the right ⇒⇒ f(3) = 2*3 - 3 = 3
∴ The function is jump discontinuous at x = 3


From the previous results the correct graph is the last as shown in attached graph.



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Hey guys! I need help with question 3.
pickupchik [31]

So firstly, you want to multiply both sides by (x-2)(x+2) since it is the LCM, or lowest common multiplier. Your equation will look like this: \frac{3}{x+2} (x-2)(x+2)-\frac{4}{x-2} (x-2)(x+2)=5(x-2)(x+2)


Next, you can cancel out the denominators on 3/x+2 and 4/x-2 on the left side: 3(x-2)-4(x+2)=5(x-2)(x+2)


Next, foil: 3x-6-4x-8=5x^2-20


Next, combine like terms: -x-14=5x^2-20


Next, add x + 14 on both sides: 0=5x^2+x-6


Next, replace x with -5x + 6x: 0=5x^2-5x+6x-6


Next, factor 5x^2-5x and 6x-6 separately. Make sure that both factors have the same quantity within the parentheses: 0=5x(x-1)+6(x-1)


With this, we can rewrite it as 0=(5x+6)(x-1) From here, we solve for x in (5x+6) and (x-1) separately and setting them to zero.


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In short, x = -1.2, 1.

3 0
3 years ago
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